0=500+6x-x^2

Solution for 0=500+6x-x^2 equation:

0=500+6x-x^2

We move all terms to the left:

0-(500+6x-x^2)=0

We add all the numbers together, and all the variables

-(500+6x-x^2)=0

We get rid of parentheses

x^2-6x-500=0

a = 1; b = -6; c = -500;
Δ = b2-4ac
Δ = -62-4·1·(-500)
Δ = 2036
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2036}=\sqrt{4*509}=\sqrt{4}*\sqrt{509}=2\sqrt{509}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{509}}{2*1}=\frac{6-2\sqrt{509}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{509}}{2*1}=\frac{6+2\sqrt{509}}{2}
$